President Reagan's proposed spending mix for next year came under fire from both parties in both houses of Congress yesterday as Democrats denounced his proposed domestic spending "freeze" and Republicans called for more cuts in military spending to ease a projected $189 billion deficit.

"There is going to be a real donnybrook . . . a ferocious debate" over defense, said Senate Majority Leader Howard H. Baker Jr. (R-Tenn.).

"I can't conceive of a freeze on domestic spending, to be perfectly truthful . . . . He's got problems with his freeze out there," said House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.).

These assessments--and an outpouring of others signaling trouble for Reagan's budget on Capitol Hill--came as the White House was stoutly contending that the president's plans, sketched out in his State of the Union message Tuesday night, were "well received on both sides of the aisle."

There was praise, in varying degrees, for the conciliatory tone of Reagan's address and some of his substantive proposals, especially those aimed at reviving the economy. But, even before the Monday due-date for delivery of his budget, the brushfires were already burning on these and other fronts:

* Senate Republican leaders met for 90 minutes with Defense Secretary Caspar W. Weinberger in an apparently unsuccessful attempt to get him to consider more cuts in military spending, a meeting that one well-placed congressional source described as "totally unproductive" and "frustrating" to most of the senators, who nevertheless plan to keep trying to work out a compromise.

* Sen. Robert J. Dole (R-Kan.) and Rep. Leon E. Panetta (D-Calif.), who head nutrition subcommittees in their respective houses, all but ruled out further cuts in the food stamp program, which Reagan cited in his speech as one of the "automatic spending programs" that he wants curtailed.

* Dole, who is also chairman of the Senate Finance Committee, said some programs, like maternal and child health, may have to be expanded instead of cut back, although he indicated support for most of Reagan's health cost-cutting plan, including limits on tax-free treatment of employer-provided health benefits.

* Some conservative Republicans, including Rep. Denny Smith (R-Ore.), joined the Democrats in criticizing Reagan's domestic spending "freeze," contending that, among other things, it should be extended to defense spending. "In order to get a freeze we have to be fair about it . . . the president's plan isn't going anywhere," said Smith.

* Reagan's proposal for a three-year standby tax increase, already spurned by Dole and Baker, got a put-down from the other side of the aisle. "I don't think we should vote for a tax increase or tax cut for somebody else's term," said Sen. Russell B. Long (D-La.), ranking minority member on the Finance Committee.

* Both O'Neill and Long called for scuttling the 10 percent income tax cut that is scheduled for July 1 under Reagan's three-year tax-cutting program and for repealing the legislation that would index income tax brackets to compensate for inflation after 1984.

O'Neill said he would push to limit tax relief that the wealthy would get from the July rate reduction or, failing that, to repeal the tax cut for everyone. Long said he would repeal it outright, calling Reagan's tax cut program a "total dud."

Amid all the budget turmoil, a potential stumbling block for the proposed Social Security rescue plan was removed yesterday as Senate Minority Leader Robert C. Byrd (D-W.Va.) and House Majority Leader James C. Wright Jr. (D-Tex.) backed off from earlier suggestions that delays in cost-of-living increases in Social Security benefits be tied to a rollback or delay in income tax cuts for the rich.

They did not mean to hold the Social Security plan hostage for tax increases on the wealthy, they hastened to assure colleagues who were dismayed by press accounts of statements they made Tuesday.

Rather, they said, they would simply try to use the Social Security cuts as leverage in arguing for income limits on the tax cut, a position that also drew O'Neill's backing.

"I expect to use it as leverage later on," after the bipartisan Social Security financing package is approved, said O'Neill, although he made it clear that he strongly opposes linking the Social Security plan to any specific action on taxes.

The Social Security package, drafted by a bipartisan commission earlier this month and endorsed by both Reagan and O'Neill, also got a boost when it was introduced yesterday in the Senate with a broad array of co-sponsors, including Sen. Edward M. Kennedy (D-Mass.), who is viewed as important in attracting liberal Democratic support for the measure.

But Kennedy and other Democrats had a field day with Reagan's budget blueprint.

Kennedy told the United Auto Workers that "the president's speechwriter must have been Charles Dickens writing about the poorhouses of Victorian times" in, as Kennedy described it, proposing "to gut Medicare, inflate military spending by 14 percent, to freeze food stamps and all domestic programs, to tax oil so families cannot afford to heat their homes."

Democratic National Chairman Charles T. Manatt said, "We Democrats would say freeze nuclear weapons, not student loans, and start asking the wealthy recipients of your tax cuts to join in national sacrifice."

While Republicans praised Reagan for moving off his earlier "stay-the-course" theme, the disparity between a 14 percent increase in military spending and a 3 percent increase for domestic programs--or an after-inflation increase of 9 percent for defense and 2 percent cut on the domestic side--was clearly one of the biggest problems for Republicans.

But, in the Senate, there were also signs of division in Republican ranks that could prove troublesome down the road. After the meeting with Weinberger, Senate Armed Services Committee Chairman John G. Tower (R-Tex.) warned that anything more than the $8 billion in defense outlay cuts that Weinberger has endorsed might jeopardize national security, while Baker said other senators were concerned about "the national fiscal risk" and want more savings from the Pentagon.

Baker has urged $15 billion in cuts as an opening bargaining position with Weinberger, saying he is not wedded to that number and hopes Weinberger is not wedded to his. However, after the meeting, participants said they detected no movement on Weinberger's part. "There was no budging at all," said one source.

Some senators have expressed fear privately that a refusal to compromise in advance of any showdown with the Democratic-controlled House could put the Democrats in a commanding position to dictate what cuts are made.

On the domestic spending side, the "freeze" that Reagan proposed appeared to be something less than that, in that it will not operate across the board. Overall, it attempts to keep spending in line with expected inflation, meaning a growth of 5 percent. But domestic programs will be held below 5 percent to compensate for the defense spending increase, which will be far greater than that.

Nor will the budget for all domestic programs rise at the same rate; some of these, too, will fare better than others. This had members of Congress in both parties who have advocated a freeze as the fairest way to cut the budget complaining that Reagan had adopted their term but not their idea.